Question: Solve for $x$ and $y$ using substitution. ${-2x-6y = -10}$ ${x = -5y+3}$
Since $x$ has already been solved for, substitute $-5y+3$ for $x$ in the first equation. ${-2}{(-5y+3)}{- 6y = -10}$ Simplify and solve for $y$ $10y-6 - 6y = -10$ $4y-6 = -10$ $4y-6{+6} = -10{+6}$ $4y = -4$ $\dfrac{4y}{{4}} = \dfrac{-4}{{4}}$ ${y = -1}$ Now that you know ${y = -1}$ , plug it back into $\thinspace {x = -5y+3}\thinspace$ to find $x$ ${x = -5}{(-1)}{ + 3}$ $x = 5 + 3$ ${x = 8}$ You can also plug ${y = -1}$ into $\thinspace {-2x-6y = -10}\thinspace$ and get the same answer for $x$ : ${-2x - 6}{(-1)}{= -10}$ ${x = 8}$